Along these lines....we've tried some varied troubleshooting on our end, but have not yet hit upon exactly what's blocking the sockets from making it to our machines. We're relatively confident that it's a firewall issue, but it's beyond simply a port - we've opened the ports and it's made no difference.
Admin, can you comment - in reading the ActionScript documentation they make mention of using XML sockets. Based on the learnings of Chagongo above, I'm assuming that the AIR application running on our end is indeed using the XML Sockets functionality mentioned in that Adobe document? (Would love to share the link, but I'm not allowed.

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I'm wondering if our firewall (a Barracuda NG device) is blocking the socket connection based on its content and not just the port. We have whitelisted the servers and IP addresses listed in the KnowledgeBase article.
The HTTP Polling doesn't appear to work for us either....but I'd rather put effort into getting the socket connection running.
Thanks!
Jarrod